I used to be able to open remote files in TextMate by mounting the remote directory via the Apple Filing Protocol [1]. Somewhere around TextMate 1.5.2 (I think), this stopped working for me. TextMate's open file dialog showed the volume as empty (?), and dragging and dropping files from the remote volume onto the TextMate icon would do nothing. Other applications, such as TextEdit, did not have these problems, so I figured this was a new TextMate bug.
I went back and loaded a copy of TextMate 1.5.1, and it worked fine. I thought this proved the issue to be a regression, but when I closed 1.5.1 and opened 1.5.3 again, it suddenly started working fine, too!
So I don't know what's going on, but if anyone has problems opening files via AFP, going back temporarily to TextMate 1.5.1 might magically fix the problem. At least it did for me.
Trevor
[1] http://comox.textdrive.com/pipermail/textmate/2006-February/ 008656.html